1. Introduction to Numerical Analysis I MATH/CMPSC 455 Loss of Significance

2. L OSS OF S IGNIFICANCE Subtracting nearly equal numbers Example : Calculate on a 3-decimal-digit computer Example : How to computer

3. L OSS OF S IGNIFICANCE Example: Quadratic formula LoS usually occurs when an operation on two numbers increases relative error substantially more than it increases absolute error

4. L OSS OF S IGNIFICANCE Theorem: If and are positive normalized binary numbers such that, and then at most and at least significant binary bits will be lost in the subtraction